1. 2.2 – Analyze Conditional Statements

2. Conditional Statement
Hypothesis
Conclusion
Logical statement written in if-then form.
If p, then q.
pq
Statement following the “if”
“p” part
Statement following the “then”
“q” part

3. Assuming “p” is true, the “q” HAS to happen
True Statement
False Statement
Counterexample
Assuming “p” is true, the “q” HAS to happen
Assuming “p” is true, the “q” might not happen. You only need ONE example to prove a statement false.
One example that proves a statement is false. When p is true, but q is false.

4. Converse
Flip the hypothesis and conclusion
If p, then q becomes If q, then p
qp
Inverse
Negate the hypothesis and conclusion
If p, then q becomes If not p, then not q
~p  ~q

5. Contrapositive
Negate the hypothesis and conclusion of the converse
If p, then q becomes If not q, then not p
~q  ~p
Equivalent to the original statement.

6. Original and converse of a statement are true.
Biconditional statement
Original and converse of a statement are true.
p if and only if q
p iff q
p  q AND q  p
pq

7. Two lines that intersect to form four right angles
Perpendicular Lines:
Two lines that intersect to form four right angles
1. Rewrite the definition of perpendicular lines in if-then form.
If two lines are perpendicular, then
they intersect to form four right angles.

8. Decide whether the statement is true or false
Decide whether the statement is true or false. If false, provide a counterexample.
If A is obtuse, then it measures 155°
False,
A is obtuse and measures 100°

9. you can be an athlete in cross-country.
State the hypothesis, conclusion, and converse. Determine if the converse is true.
If you are a football player, then you are an athlete.
hypothesis
conclusion
Converse:
If you are a athlete, then you are a football player.
False,
you can be an athlete in cross-country.

10. State the hypothesis, conclusion, and converse
State the hypothesis, conclusion, and converse. Determine if the converse is true.
If x = 3, then x2 = 9.
hypothesis
conclusion
Converse:
If x2 = 9, then x = 3.
False,
x2 = 9 and x = -3

11. A car runs when there is gas in the tank.
4. Rewrite the statement in if-then form. Then write the converse, the inverse, and the contrapositive.
A car runs when there is gas in the tank.
If-then:
If a car is running, then there is gas in the tank.
Converse:
If there is gas in the tank, then the car is running.
Inverse:
If the car isn’t running, then there isn’t gas in the tank.
Contra:
If there isn’t gas in the tank, then the car isn’t running.

12. All triangles have three sides.
4. Rewrite the statement in if-then form. Then write the converse, the inverse, and the contrapositive.
All triangles have three sides.
If-then:
If a polygon is a triangle, then it has 3 sides.
Converse:
If a polygon has 3 sides, then it is a triangle.
Inverse:
If a polygon isn’t a triangle, then it doesn’t have 3 sides.
Contra:
If a polygon doesn’t have 3 sides, then it isn’t a triangle.

13. 5. Rewrite the definition as a biconditional statement.
Two angles are complementary angles when the sum of their measures is 90°
Two angles are complementary angles IFF their sum measures 90°

14. 5. Rewrite the definition as a biconditional statement.
Equilateral polygons have all of their sides congruent.
A polygon is equilateral IFF all of the sides are congruent

15. 6. Determine if the if-then statement is true or false
6. Determine if the if-then statement is true or false. If false, provide a counterexample.
If you drive a mustang, then it is red.
False,
You drive a mustang that is black.

16. 6. Determine if the if-then statement is true or false
6. Determine if the if-then statement is true or false. If false, provide a counterexample.
If T is between S and R, then ST + TR = TS. R S T
False,
T is between S and R, then ST + TR = SR

17. 6. Determine if the if-then statement is true or false
6. Determine if the if-then statement is true or false. If false, provide a counterexample.
If m2 = 90°, then it is a right angle.
True

18. 7. Decide whether each statement about the diagram is true
7. Decide whether each statement about the diagram is true. Explain your answer.
mAEB = 90°
True,
it is a right angle

19. 7. Decide whether each statement about the diagram is true
7. Decide whether each statement about the diagram is true. Explain your answer.
AE + EC = 180°
False,
Segments aren’t measured in degrees!

20. 7. Decide whether each statement about the diagram is true
7. Decide whether each statement about the diagram is true. Explain your answer.
AED  BEC
True,
Vertical Angles

21. “If there is a fire, then a fish dies”
THE FIRE-FISH STORY
“If there is a fire, then a fish dies”
You are to write a creative story consisting entirely of conditional statements.
The first statement should be of the form: “If there is a fire, then A.”
The second statement should be of the form: “If A, then B.”
The hypothesis of each statement must be the conclusion of the previous statement.
The story must be out of at least 5 conditional statements, ending with “If D, then a fish dies.”

22. If there is a fire, then ___________________________________.
If ________________, then …………………………………
If …………………………., then ***************************************.
If *******************************, then xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx.
If xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx, then a fish dies.

23. An angle measures between 90° and 180° IFF it is obtuse
HW Problem
2.2
82-85
1-15 odd, 16-18, odd
# 19
Ans:
An angle measures between 90° and 180° IFF it is obtuse